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%I #19 Jan 17 2019 02:55:13
%S 3,11,31,83,283,383,1327,2591,7351,7759,11171,11587,31391,46919,
%T 147919,288023,360611,425603,507163,666203,1414703,2198887,3358151,
%U 9287659,11512547,11648531,24315047,42453823,145554779,161720147,184007671,766668811
%N Primes 4k + 3 preceding the maximal gaps in A268799.
%C Subsequence of A002145.
%C A268799 lists the corresponding record gap sizes. See more comments there.
%H Alexei Kourbatov, <a href="/A268800/b268800.txt">Table of n, a(n) for n = 1..41</a>
%H Alexei Kourbatov and Marek Wolf, <a href="http://arxiv.org/abs/1901.03785">Predicting maximal gaps in sets of primes</a>, arXiv preprint arXiv:1901.03785 [math.NT], 2019.
%e The first two primes of the form 4k+3 are 3 and 7, so a(1)=3. The next prime of this form is 11; the gap 11-7 is not a record so no term is added to the sequence. The next prime of this form is 19; the gap 19-11=8 is a new record so a(2)=11.
%o (PARI) re=0; s=3; forprime(p=7, 1e8, if(p%4!=3, next); g=p-s; if(g>re, re=g; print1(s", ")); s=p)
%Y Cf. A002145, A084161, A268799, A268801.
%K nonn
%O 1,1
%A _Alexei Kourbatov_, Feb 13 2016
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